揭示了置信预测与场景优化的理论联系，统一了两类决策验证方法。
Bridging conformal prediction and scenario optimization
- 通过选择合适评分函数，将置信预测转化为场景优化问题。
- 证明了置信预测可恢复场景程序的约束违反概率上界。
- 为校准置信预测提供了新分析视角，适合关注决策可靠性的研究者。
置信预测与场景优化是两类重要的统计学习框架，用于数据驱动决策的可靠性验证，在控制理论、机器学习和机器人等领域有广泛应用。尽管两者研究活跃且结果相似，但它们之间的清晰联系尚未建立。本文聚焦于基础置信预测，严格证明如何选择适当的评分函数并设定预测映射，以恢复场景规划中约束违反概率的经典上界。同时，将非一致性评分排序视为一维场景程序（忽略部分约束），利用该联系重新获得基础置信预测对集合预测有效性的保证。此外，结合场景方法的核心成果，进一步分析了条件校准置信预测。研究结果建立了置信预测与场景优化之间的理论桥梁。
原文摘要 · Abstract (English)
Conformal prediction and scenario optimization constitute two important classes of statistical learning frameworks to certify decisions made using data. They have found numerous applications in control theory, machine learning and robotics. Despite intense research in both areas, and apparently similar results, a clear connection between these two frameworks has not been established. By focusing on the so-called vanilla conformal prediction, we show rigorously how to choose appropriate score functions and set predictor map to recover well-known bounds on the probability of constraint violation associated with scenario programs. We also show how to treat ranking of nonconformity scores as a one-dimensional scenario program with discarded constraints, and use such connection to recover vanilla conformal prediction guarantees on the validity of the set predictor. We also capitalize on the main developments of the scenario approach, and show how we could analyze calibration conditional conformal prediction under this lens. Our results establish a theoretical bridge between conformal prediction and scenario optimization.
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